Certain conventional dropper bottles are made from a relatively soft plastic resin; filled with a liquid, such as an eye medicine; and shipped from the factory with the top of the bottle sealed to preserve the liquid until it is to be dispensed from the bottle. As shown in FIGS. 7a-c, the top of such a bottle is pierced by the user when the bottle is to be used for the first time. Referring now to FIG. 7a, the bottle is shipped with a piercing cap 71 partially screwed in place, and the top 70 of the bottle unpierced. The cap 71 is then screwed down onto the bottle top 70 by the user, and a spike 71a integrally formed with the cap 71 pierces the top 70 of the bottle (see FIG. 7b). The user then unscrews the cap 71 completely, leaving the pierced top 70 of the bottle exposed, and the bottle ready to dispense drops of the liquid.
While the piercing cap arrangement of FIGS. 7a-c may be adequate for liquids of a certain viscosity range, relatively viscous liquids require a dropper bottle tip having a precise size and shape, which is difficult or impossible to produce from a spike piercing the top of a bottle. As a result, such liquids cannot be successfully dispensed from the conventional bottle and cap arrangement shown in FIGS. 7a-c. 